Train Speed Problem: Same Direction Calculation

This problem involves two trains moving in the same direction. We need to find the distance from point Y to the meeting point Z using their speeds and the initial distance between them.

Calculating Relative Speed

When two objects move in the same direction, their relative speed is the difference between their individual speeds. This relative speed indicates how quickly the faster object gains on the slower one.

• Speed of Train 1 (from X): $S_1 = 32\text{ km/h}$
• Speed of Train 2 (from Y): $S_2 = 26\text{ km/h}$
• Relative Speed ($S_{rel}$): $S_1 - S_2 = 32\text{ km/h} - 26\text{ km/h} = 6\text{ km/h}$

Determining Time to Meet

The faster train (from X) needs to cover the initial distance separating them ($42\text{ km}$) at their relative speed to catch up with the slower train (from Y). We can calculate the time ($t$) it takes for this to happen.

Time ($t$) = Initial Distance / Relative Speed

Finding Distance from Y to Z

The meeting point Z is beyond Y. The distance from Y to Z ($D_{YZ}$) is the distance covered by the slower train (Train 2) in the calculated time ($t$).

Distance ($D_{YZ}$) = Speed of Train 2 ($S_2$) $\times$ Time ($t$)

Therefore, the distance from Y to Z is $182\text{ km}$.